{"paper":{"title":"Full-Spectrum Graph Neural Networks: Expressive and Scalable","license":"http://creativecommons.org/licenses/by/4.0/","headline":"FSpecGNN lifts classical spectral GNNs to the node-pair domain using bivariate filters over eigenvalue pairs, recovering the old models as a diagonal case while reaching universal approximation of node-pair signals.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Deyu Bo, Kelin Xia, Longlong Li, Xiaohan Wang","submitted_at":"2026-05-07T06:53:49Z","abstract_excerpt":"It is well established that spectral graph neural networks (GNNs) can universally approximate node signals; however, their expressive power remains bounded by the 1-dimensional Weisfeiler-Lehman test, which is mirrored in their lack of universality for higher-order signals. To go beyond this bound, we propose the Full-Spectrum GNNs (FSpecGNNs), a second-order generalization of classical spectral GNNs. FSpecGNN advances spectral filtering from two perspectives: (1) it lifts signals from the node domain to the node-pair domain; and (2) it extends the univariate spectral filter over eigenvalues t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that classical spectral GNNs arise as a diagonal special case of FSpecGNN, and prove that FSpecGNN can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the low-rank approximation of the full-spectrum convolution preserves both the universal approximation property for node-pair signals and the claimed expressivity bound without introducing errors that invalidate the theoretical results on realistic graphs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"FSpecGNN generalizes spectral GNNs to node-pair domain with bivariate filters, achieving universal approximation of node-pair signals while remaining at most as expressive as Local 2-GNN and admitting scalable low-rank implementations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"FSpecGNN lifts classical spectral GNNs to the node-pair domain using bivariate filters over eigenvalue pairs, recovering the old models as a diagonal case while reaching universal approximation of node-pair signals.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"cc8774462bd94fcd0dcb89c4e1b9cbf9c6a15aa3f09a984132327088f8764a07"},"source":{"id":"2605.05759","kind":"arxiv","version":2},"verdict":{"id":"5707001d-d420-43c5-b9df-cfa82b3fc18d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T14:51:22.625269Z","strongest_claim":"We show that classical spectral GNNs arise as a diagonal special case of FSpecGNN, and prove that FSpecGNN can be at most as expressive as Local 2-GNN while universally approximating node-pair signals, the latter being particularly beneficial for heterophilic graph learning.","one_line_summary":"FSpecGNN generalizes spectral GNNs to node-pair domain with bivariate filters, achieving universal approximation of node-pair signals while remaining at most as expressive as Local 2-GNN and admitting scalable low-rank implementations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the low-rank approximation of the full-spectrum convolution preserves both the universal approximation property for node-pair signals and the claimed expressivity bound without introducing errors that invalidate the theoretical results on realistic graphs.","pith_extraction_headline":"FSpecGNN lifts classical spectral GNNs to the node-pair domain using bivariate filters over eigenvalue pairs, recovering the old models as a diagonal case while reaching universal approximation of node-pair signals."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05759/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T13:42:04.674408Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T09:35:50.470497Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:19.501599Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:17:58.367695Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6f7688238a30e38ac5420e8d728b6f4c77f1d935abbb05b1882d10561c16fee0"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}